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Abbott reminds Senate of his mandate

Prime Minister Tony Abbott has again reminded the Senate his government was elected to rein in the budget and repeal the carbon tax.

Incoming crossbench senators David Leyonhjelm, from the Liberal Democratic Party, and Family First's Bob Day have told The Australian they oppose the coalition's plans to stop a second increase to the tax-free threshold.

"The Liberal Democrats will never vote for an increase in taxes and, therefore, we won't vote to reverse a tax cut," Mr Leyonhjelm told the newspaper.

Mr Abbott said he'd like nothing more than to be able to give another "swift round of tax cuts" but the fiscal position made that difficult.

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"Obviously we're going to talk respectfully to the crossbench senators," he told reporters in Ottawa, Canada.

"But we also expect them to respect the fact the government has a job to do ... to bring the budget back under control as well as to repeal the carbon tax."

Without the carbon tax there was "much less need" for associated compensation, he said.

The tax-free threshold has already increased from $6000 to $18,200 and Labor planned to further lift it to $19,400 as part of its carbon tax compensation.

At least one crossbench senator has been told the Abbott government intends to repeal this second increase, The Australian reported.